From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

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Solution

Here, we need to permute 2 teachers out of the 36 available teachers.
It can also be understood as the arrangement of 36 teachers, taken two at a time.
∴ Required number of ways = ³⁶P₂
$= \frac{36!}{(36 - 2)!} = \frac{36!}{34!} = \frac{36 \times 35 \times 34!}{34!} = 36 \times 35 = 1260$

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From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

Here, we need to permute 2 teachers out of the 36 available teachers. It can also be understood as the arrangement of 36 teachers, taken two at a time. ∴ Required number of ways = 36P2 =36!36-2!=36!34!=36×35×34!34!=36×35 = 1260

Here, we need to permute 2 teachers out of the 36 available teachers.
It can also be understood as the arrangement of 36 teachers, taken two at a time.
∴ Required number of ways = ³⁶P₂
$= \frac{36!}{(36 - 2)!} = \frac{36!}{34!} = \frac{36 \times 35 \times 34!}{34!} = 36 \times 35 = 1260$